Interpolation for geochemical surface reconstruction incorporating topographic catchment definitions

Geochemical surfaces are reconstructed by interpolating geochemical measurements obtained from stream-water and stream-sediment samples. The geographical region that influences (and therefore is represented by) the value of a geochemial sample is its topographic catchment area. However, standard convention is to treat and to record the stream sample in the database as a point location, and to reconstruct geochemical surfaces utilizing conventional point interpolation procedures. These interpolation procedures assume, generally, that a data point exerts geographical influence away from itself in all directions, and that influence declines with distance away from that data point. Conventional interpolation procedures are poorly suited for reconstructing geochemical surfaces from stream samples; they do not take into account the true geographic area that geochemical sample points represent (topographic catchments). In this paper we propose a method of interpolation which assumes that data points are representative of their topographic catchment areas. Experimental data indicates that a surface reconstruction procedure which preserves the areal character of geochemical samples provides results more meaningful than surfaces reconstructed using more conventional interpolation techniques.